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Security market line? (SML) Assume that the? risk-free rate, RF?, is currently 4?% and that the market? return, rm?, is currently 7?%
Security market line? (SML) Assume that the? risk-free rate, RF?, is currently 4?% and that the market? return, rm?, is currently 7?%.
a. Calculate the market risk premium.
b. Given the previous? data, calculate the required return on asset A having a beta of 0.4 and asset B having a beta of 1.5.
1. The market risk premium is ...??%. ?(Round to one decimal? place.)
2. If the beta of asset A is 0.4?, the required return for asset A is ....??%. ?(Round to one decimal? place.)
If the beta of asset B is 1.5?, the required return for asset B is ....?%. ?(Round to one decimal? place.)
No2.
Manipulating CAPM Use the basic equation for the capital asset pricing model ?(CAPM?) to work each of the following problems.
a. Find the required return for an asset with a beta of 0.49 when the? risk-free rate and market return are 3?% and 8%?, respectively.
b. Find the ?risk-free rate for a firm with a required return of 11.184?% and a beta of 1.09 when the market return is 11%.
c. Find the market return for an asset with a required return of 11.761?% and a beta of 1.17 when the? risk-free rate is 9%.
d. Find the beta for an asset with a required return of 12.764?% when the? risk-free rate and market return are 7?% and 11.4%?, respectively.
1. The required return for an asset with a beta of 0.49 when the? risk-free rate and market return are 3?% and 8%?, ?respectively, is ....?%. ?(Round to two decimal? places.)
2. The? risk-free rate for a firm with a required return of 11.184?% and a beta of 1.09 when the market return is 11% is ...?%. ?(Round to two decimal? places.)
3. The market return for an asset with a required return of 11.761?% and a beta of 1.17 when the? risk-free rate is 9% is ......?%. ?(Round to two decimal? places.)
4. The beta for an asset with a required return of 12.764?% when the? risk-free rate and market return are 7?% and 11.4%?, ?respectively, is .....? ?(Round to two decimal? places.)
Expert Solution
Security market line? (SML):
1) Computation of Market Risk Premium:
Market Risk Premium = Market Return - Risk-free Rate
= 7% - 4%
= 3%
2) Computation of Required Rate of Return on Asset A and Asset B:
Required Rate of Return = Risk-free Rate + Beta*Market Risk Premium
For Asset A:
Required Rate of Return = 7% + 0.4*3%
= 7% + 1.20%
Required Rate of Return = 8.20%
For Asset B:
Required Rate of Return = 7% + 1.5*3%
= 7% + 4.50%
Required Rate of Return = 11.50%
Manipulating CAPM:
a) Computation of Required Rate of Return for an Asset:
Required Rate of Return = Risk-free Rate + Beta*Market Risk Premium
= 3% + 0.49*(8%-3%)
= 3% + 0.49*5%
= 3% + 2.45%
Required Rate of Return = 5.45%
b) Computation of Risk-free Rate:
Required Rate of Return = Risk-free Rate + Beta*Market Risk Premium
11.184% = x + 1.09*(11% - x)
11.184% = x + 0.1199 - 1.09x
11.184% - 0.1199 = -0.09x
-0.00806 = -0.09x
x = -0.00806/-0.09
x = 8.9556% or 8.96%
So, Risk-free Rate is 8.96%
c) Computation of Market Return for an Asset:
Required Rate of Return = Risk-free Rate + Beta*Market Risk Premium
11.761% = 9% + 1.17*(x - 9%)
11.761% - 9% = 1.17x - 10.53%
11.761% - 9% + 10.53% = 1.17x
13.291% = 1.17x
x = 13.291% / 1.17
x = 11.36%
So, Market Return is 11.36%.
d) Computation of Beta for an Asset:
Required Rate of Return = Risk-free Rate + Beta*Market Risk Premium
12.764% = 7% + x * (11.4% - 7%)
12.764% - 7% = x*4.4%
5.764% = x*4.4%
x = 5.764%/4.4%
x = 1.31
So, Beta for an asset is 1.31
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